NEW CRITICAL IMPURITY DENSITY IN METAL-INSULATOR TRANSITION, OBTAINED IN N(P)- TYPE DEGENERATE HELIUM-FERMI LIQUID, BEING JUST THAT OF THE CARIERS, LOCALIZED IN EXPONENTIAL BAND TAILS. (IX)

By basing on the same physical model and treatment method, as used in our recent work[1], we will investigate the critical impurity densities in the metal-insulator transition (MIT), obtained in n(p)-type degenerate Helium-Fermi Liquid (He-FL), being due to the effects of the size of donor (acceptor) d(a)-radius, , and the high d(a)-density, N, assuming that all the impurities are ionized even at T=0 K. In such the n(p)-type He-FL, some important remarks are obtained and discussed in the following. (i)-In Tables 1a-1d in Appendix 1, the numerical results of the isothermal bulk modulus, , the pressure variation, , and the strain-energy variation, , are obtained and computed, using Equations (2, 3). It should be noted that, for a given, those increase with increasing reduced effective mass, in good agreement with Landau’s remarks on the Fermi Liquid.[2] (ii)-In Tables 2a-5d in Appendix1, the numerical results of the critical impurity density in the metal-insulator transition (MIT), as that given in Eq. (8), by using an empirical Mott parameter , are obtained and discussed. (iii)-Further, also in Tables 2a-5d in Appendix 1, for a given , the numerical results of the density of electrons (holes) localized in the exponential conduction (valence)-band tails (EBT), , are obtained, using Eq. (26), and taking the empirical Heisenberg parameter, , as that given in Eq. (15), giving raise to: with a precision of the order of , as that given in Table 3a in Appendix 1. In other words, such the critical d(a)-density is just the density of electrons (holes) localized in the EBT, , respectively.